@Article{NMTMA-10-597,
author = {Cuicui Ji and Zhizhong Sun},
title = {An Unconditionally Stable and High-Order Convergent Difference Scheme for Stokes' First Problem for a Heated Generalized Second Grade Fluid with Fractional Derivative},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2017},
volume = {10},
number = {3},
pages = {597--613},
abstract = {<p style="text-align: justify;">This article is intended to fill in the blank of the numerical schemes with second-order
convergence accuracy in time for nonlinear Stokes&#39; first problem for a heated generalized second grade
fluid with fractional derivative. A linearized difference scheme is proposed.
The time fractional-order derivative is discretized by second-order shifted and weighted
Grünwald-Letnikovv difference operator. The convergence accuracy
in space is improved by performing the average operator. The presented numerical method
is unconditionally stable with the global convergence order of&nbsp;$\mathcal{O}(τ^2+h^4)$ in maximum norm,
where&nbsp; $τ$ and $h$ are the step sizes in time and space, respectively.
Finally, numerical examples are carried out to verify the theoretical results, showing that our scheme is
efficient indeed.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2017.m1605},
url = {http://global-sci.org/intro/article_detail/nmtma/12360.html}
}